Ryan Giggs' side had dismantled Republic of Ireland in the group opener days earlier, but against Denmark - at full strength after resolving their sponsorship row - they lacked a cutting edge.
Gareth Bale, wearing the captain's armband, struggled to influence play and Eriksen instead proved the difference with a fine first-half strike and a penalty after the break.
This functional Denmark side profited on the occasional Welsh mistake to take two big chances, handing out a lesson in competitive internationals to opponents depending again on young talents like Ethan Ampadu.
Thomas Delaney and Bale sent left-footed drives fizzing wide at either end in a low-key opening half-hour, but Eriksen was clinical when his first opening arrived.
The Tottenham man controlled in the area to drill against the foot of the post and in, with only an instinctive one-handed Wayne Hennessey stop then keeping Pione Sisto from lashing in a quick second.
Wales started the second half on the front foot but made little of their bright spell, unable to create a chance akin to that which Martin Braithwaite passed up after wriggling past Chris Mepham in the visitors' box.
Once more, though, Eriksen would take his opportunity. Ampadu was penalised for handling Viktor Fischer's cross and the spot-kick, taken by Eriksen, was smashed home to clinch victory.
Delaney and Eriksen threatened to extend Denmark's advantage late on but Hennessey was on hand to keep the score respectable.
What does it mean: Another Welsh reality check
For the second time in Giggs' short reign, Wales followed up a devastating win with a hard-fought defeat against better opposition. Playing in League B, the visitors have time to learn and improve, but this was a reminder that Wales are still not at the same level as a Denmark side that did not pull up any trees at the World Cup.
Pat on the back: Danes' difference-maker delivers
Much was made of how Tottenham spent 'the Gareth Bale money', but Eriksen has proven an unmitigated success in England. The Spurs star is Denmark's main man, too, and it was he, not Bale, who lifted the game from its first-half slumber. A brilliant Eriksen goal proved to be the one moment of real quality, while he was clinical from the spot.
Boot up the backside: Stars of Ireland win struggle
Ampadu and Bale took Ireland apart earlier this week, but neither enjoyed the best of days in Aarhus. The 17-year-old was out of position for Eriksen's first and conceded the penalty for the second, while his stand-in skipper could not escape the attentions of a rugged Denmark defence, only threatening once early on.
Key Opta Facts- Wales have lost a competitive fixture away from home for the first time since a 0-2 defeat to Bosnia-Herzegovina back in October 2015.
- Denmark are now unbeaten in each of their last 11 home matches in all competitions (W5 D6) since a 0-1 loss to Montenegro back in October 2016.
- Wales have failed to score in three of their last four games in all competitions (W1 D1 L2), as many instances as in their previous 13 such matches.
- Denmark have kept seven clean sheets in their last nine home matches, conceding just two goals in that time.
- Ryan Giggs has lost two of his first five matches in charge (W2 D1), as many defeats as Wales suffered in the previous 12 games prior to his appointment (P12 W4 D6 L2).
- Christian Eriksen has been directly involved in 20 goals in his last 18 appearances for Denmark (15 goals, 5 assists).
5 - Since Mark Hughes’ win in Belarus back in September 1999, each of the last five Wales managers have lost their first competitive match away from home (also John Toshack, Brian Flynn, Gary Speed and Chris Coleman). Repetition. pic.twitter.com/iT9nSGDC0n— OptaJoe (@OptaJoe) September 9, 2018